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Numerical Relativity
  • Language: en
  • Pages: 717

Numerical Relativity

Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. Assuming only a basic knowledge of classical general relativity, the book develops the mathematical formalism from first principles, and then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. The book contains 300 exercises to help readers master new material as it is presented. Numerous illustrations, many in color, assist in visualizing new geometric concepts and highlighting the results of computer simulations. Summary boxes encapsulate some of the most important results for quick reference. Applications covered include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and other topics of current physical and astrophysical significance.

Numerical Relativity: Starting from Scratch
  • Language: en
  • Pages: 235

Numerical Relativity: Starting from Scratch

A pedagogical and accessible introduction to numerical relativity, the key tool to model gravitational waves and black hole mergers.

3+1 Formalism in General Relativity
  • Language: en
  • Pages: 304

3+1 Formalism in General Relativity

  • Type: Book
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  • Published: 2012-02-27
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  • Publisher: Springer

This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented,...

Problem Book in Relativity and Gravitation
  • Language: en
  • Pages: 616

Problem Book in Relativity and Gravitation

An essential resource for learning about general relativity and much more, from four leading experts Important and useful to every student of relativity, this book is a unique collection of some 475 problems--with solutions--in the fields of special and general relativity, gravitation, relativistic astrophysics, and cosmology. The problems are expressed in broad physical terms to enhance their pertinence to readers with diverse backgrounds. In their solutions, the authors have attempted to convey a mode of approach to these kinds of problems, revealing procedures that can reduce the labor of calculations while avoiding the pitfall of too much or too powerful formalism. Although well suited for individual use, the volume may also be used with one of the modem textbooks in general relativity.

Relativistic Hydrodynamics
  • Language: en
  • Pages: 752

Relativistic Hydrodynamics

This book provides an up-to-date, lively and approachable introduction to the mathematical formalism, numerical techniques and applications of relativistic hydrodynamics. The topic is presented here in a form which will be appreciated both by students and researchers in the field.

The Finite-Difference Modelling of Earthquake Motions
  • Language: en
  • Pages: 387

The Finite-Difference Modelling of Earthquake Motions

A systematic tutorial introduction to the finite-difference (FD) numerical modelling technique for professionals, academic researchers, and graduate students in seismology.

Sidney Coleman's Lectures on Relativity
  • Language: en
  • Pages: 261

Sidney Coleman's Lectures on Relativity

This book is based on a graduate course on relativity given by Sidney Coleman at Harvard during the 1960s.

General Relativity and Gravitation
  • Language: en
  • Pages: 697

General Relativity and Gravitation

Explore spectacular advances in contemporary physics with this unique celebration of the centennial of Einstein's discovery of general relativity.

A General Relativity Workbook
  • Language: en

A General Relativity Workbook

  • Type: Book
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  • Published: 2015-03-06
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  • Publisher: Unknown

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Rotating Relativistic Stars
  • Language: en
  • Pages: 435

Rotating Relativistic Stars

The masses of neutron stars are limited by an instability to gravitational collapse and an instability driven by gravitational waves limits their spin. Their oscillations are relevant to x-ray observations of accreting binaries and to gravitational wave observations of neutron stars formed during the coalescence of double neutron-star systems. This volume includes more than forty years of research to provide graduate students and researchers in astrophysics, gravitational physics and astronomy with the first self-contained treatment of the structure, stability and oscillations of rotating neutron stars. This monograph treats the equations of stellar equilibrium; key approximations, including slow rotation and perturbations of spherical and rotating stars; stability theory and its applications, from convective stability to the r-mode instability; and numerical methods for computing equilibrium configurations and the nonlinear evolution of their oscillations. The presentation of fundamental equations, results and applications is accessible to readers who do not need the detailed derivations.